If A = Σ 1/(3 + (-1)^n)^n, n ∈ (1, ∞ ) and B = Σ (-1)^n/(3 + (-1)^n)^n, n ∈ (1, ∞) then A/B is equal to :

Question

If \(A=\sum\limits_{n=1}^{\infty}\frac{1}{(3 + (-1)^n)^n}\) , 

Σ 1/(3 + (-1)ⁿ)ⁿ, n ∈ (1, ∞ ) and  \(B=\sum\limits_{n=1}^{\infty}\frac{(-1)^n}{(3 + (-1)^n)^n}\), then A/B is equal to:

(A) 11/9

(B) 1

(C) -11/9

(D) -11/3

Answer 1

Correct option is (C) -11/9